{"docId":5106,"paperId":5106,"url":"https:\/\/hrj.episciences.org\/5106","doi":"10.46298\/hrj.2019.5106","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986071","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01986071v1","dateSubmitted":"2019-01-23 14:14:43","dateAccepted":"2019-01-23 15:31:08","datePublished":"2019-01-23 15:31:19","titles":{"en":"On-Regular Bipartitions Modulo $m$"},"authors":["Somashekara , D D","Vidya , K N"],"abstracts":{"en":"Let $b_l (n)$ denote the number of $l$-regular partitions of $n$ and $B_l (n)$ denote the number of $l$-regular bipartitions of $n$. In this paper, we establish several infinite families of congruences satisfied by $B_l (n)$ for $l \\in {2, 4, 7}$. We also establish a relation between $b_9 (2n)$ and $B_3 (n)$."},"keywords":[["05A17"],["Congruence"],["partition"],["regular partition"],["regular bipartition"],["theta functions 2010 Mathematics Subject Classification 11P83"],"[ MATH ] Mathematics [math]","[ MATH.MATH-NT ] Mathematics [math]\/Number Theory [math.NT]"]}